Contracts as games on event structures

Abstract

Event structures are one of the classical models of concurrent systems. The idea is that an enabling X |- e represents the fact that\ud the event e can only occur after all the events in the set X have already occurred. By interpreting events as actions promised by some participants, and by associating each participant with a goal (a function on sequences of events), we use event structures as a formal model for contracts. The states of a contract are sequences of events; a participant has a contractual obligation (in a given state) whenever some of its events is enabled in such a state. To represent the fact that participants are mutually distrusting, we study concurrent games on event structures; there, participants may play by firing events in order to reach their goals, and eventually win, lose or tie.\ud A crucial notion arising in this setting is that of agreement: a participant agrees on a set of contracts if she has a strategy to reach her goals in all the plays conforming to her strategy (or to make another participant sanctionable for not honouring an obligation). Another relevant notion is protection: a participant is protected by her contract when she has a strategy to avoid losing in any contexts, even in those where she has not reached an agreement. We study conditions for obtaining agreement and protection, and we show that these properties mutually exclude each other in a certain class of contracts. We then relate the notion of agreement in contracts with that of compliance in session types. In particular, we show that compliance corresponds to the fact that eager strategies lead to agreement

Automata for Specifying and Orchestrating Service Contracts

“…Contracts are represented in [6] through Event Structures endowed with certain notions from Game Theory. An agreement property is proposed, ensuring safe interactions among participants, that is similar to ours under an eager strategy.…”

Combining behavioural types with security analysis

“…The notion of agreement in the game-based model is related in [7] to the progressbased notion of compliance in session types [5]. More precisely, two session types are compliant if and only if, in their interpretation as ESs, all (innocent) strategies are winning.…”

“…A dishonest broker could make Player 3 interact with another player with session type: While, in general, it is not always possible to guarantee that a set of contracts admit both agreement and protection (as proved in [7]), it is possible to reconcile these two notions by relaxing the classical notion of causality, i.e., by assuming that some events can occur in the absence of a causal justification in the past, provided they have a justification in the future [8].…”

Debits and Credits in Petri Nets and Linear Logic

“…This is a classical issue, discussed by philosophers at least since Hobbes' Leviathan [1], and more recently dealt with by several works in the area of concurrency theory, e.g. [2,3,4,5,6,7].…”